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THE WAVE EQUATION
THE DIFFUSION EQUATION
1 other sections not shown
applied arbitrary constants assume behaviour boundary conditions bu/bt bu/bx cable Chapter characteristics coefficients consider const convergent coordinates corresponding curves cylinder D'Alembert's solution defined denote determined diffusion equation Dirichlet problem discontinuities discussed in Section displacement ditions drawn in Fig energy equation 3.1 example Exercise finite fluid Fourier series Fourier sine series function given harmonic heat flow Hence hyperbolic incident wave independent variables infinite initial and boundary initial conditions initial value integral irrotational kinetic Laplace's equation linear mass mathematical mesh points method normal derivative obtain one-dimensional ordinary differential equations oscillations parabolic partial differential equations physical plane poker prescribed pressure region represent result satisfies Section 2.3 separation of variables slab solution of Laplace's steady string surface temperature distribution term-by-term theorem transmitted wave unique unit area unit length vanishes vector velocity potential viscosity wall wave equation x-axis zero